Dimensions

He spins you around for fun, and puts you back when he's done, but off by a hundredth of a degree. Depending on how strict your interpretation is, you either no longer exist in the same 3D universe except at that single point of intersection, or you will drift off from it the further you move from your current location.

This is a comic adaptation of the 1884 (that's not a typo) Flatland, but in the book, instead of rotating, they explain the concept of the next higher dimension. Similar result. Good book, nails the social satire of sexism (remains relevant today).

Fun fact, the Mandelbrot set is a 2-dimensional set (because it's defined in the complex plane). However, its boundary line is a fractal, which can be understood as having a non-integer dimension (i.e., between 1, the topological dimension of a line, and 2, the dimension of a plane). There are multiple ways to define fractal dimensions such as the Hausdorff dimension. For example, the Sierpinski triangle has a Hausdorff dimension of 1.58. But the Mandelbrot set is special here, too, as it seems to have a Hausdorff dimension of 2, meaning that its boundary is so curly that it fills "a plane's worth of space" despite its line-like topology.

Silly, the Mandelbrot set is just 2D. Payback's a bitch, motherfucker.

Eh, there's probably worse ways to go insane.

You know the weirdest shit about fractals is that if the fractal is space filling (you repeated the pattern at all scales for infinity and end up filling a 2d area with lines somehow than that fractal exists between the integers definitions of dimensions). A 1d simple line fractal pattern can through the bullshit magic of math have a dimensionality of 1.65 or whatever, it is weird shit.

I am sure I got something wayyyy wrong about this lol, but whatever.

Theese captchas